CN110457772A - The DEM of a kind of combination planar curvature and steepest direction of fall flows to estimation method - Google Patents
The DEM of a kind of combination planar curvature and steepest direction of fall flows to estimation method Download PDFInfo
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Abstract
The present invention provides the DEM of a kind of combination planar curvature and steepest direction of fall to flow to estimation method, comprising the following steps: step S1: load digital elevation model;Step S2: the planar curvature of 3 vertex units of triangle projective planum where calculating steepest direction of fall;Step S3: steepest direction of fall is adjusted using the ratio of the planar curvature of step S2 3 units being calculated.The invention has the benefit that present invention incorporates planar curvatures and steepest direction of fall, a kind of method for estimating digital elevation model water (flow) direction is invented, compared to traditional direct method using steepest direction of fall, this method has precision higher, it is more preferable to convergent main river reduction effect, consider the advantage of hypsography variation, while the step of this method increases with respect to conventional method is few, will not cause the difference of too many computer running time.
Description
Technical field
The present invention relates to digital Terrain Analysis technical field more particularly to a kind of combination planar curvature and steepest direction of falls
DEM flow to estimation method.
Background technique
Water (flow) direction refers to the moving direction of water, soil, solute under the effect of gravity at the earth's surface, is much water
The parameter that must determine in literature, the numerical simulation in geomorphology field.Since true complicated landform can not be stored completely into meter
Calculation machine, therefore current hydrology landform model is mainly using digital elevation model as terrain source data, the calculating of water (flow) direction
Generally carried out based on digital elevation model.
O ' Callaghan and Mark proposed earliest water (flow) direction calculation method in 1984, by comparing center list
The gradient between first and 8 adjacent cells is chosen the maximum adjacent cells of the gradient between center cell as downstream units, by center
The flow direction of unit is directed toward the unit midpoint.Since this method only allows to choose flow direction from 8 directions, it is referred to as from all directions
To (D8) method.Since true water (flow) direction may not be one of 8 permission directions, there are large errors for D8 method.
In order to reduce the error of D8 method, Tarboton (1997) proposes that constructing 8 triangles with center cell and 8 adjacent cells puts down
Face determines method of the steepest direction of fall as water (flow) direction, the water (flow) direction being calculated using this method can for 0 °-
Any value between 360 °, precision are greatly improved compared to D8 method.This method is named as infinite flow direction (Dinf) method.However
Since Dinf method has ignored bending fluctuation existing for landform during constructing triangle projective planum, in landform and uneven
Smooth is to equally exist error, and especially when landform bending degree is larger, error is particularly acute.Hooshyar et al. was in 2016
The method using tangential curvature adjustment steepest direction of fall is proposed, but their method is only applicable to optimization convergence type landform
Flow direction.Restoring topographical surface by math equation due to completely, simultaneously use direction derivative obtains the theoretical method of flow direction in reality
In be difficult to realize, therefore can only use certain method that steepest direction of fall is adjusted so as to closer to true flow direction.
Currently used topography curvature mainly has planar curvature, profile curvature, 3 kinds of tangential curvature, wherein planar curvature energy
It is enough well reflected landform diverging, convergent degree, including can not during a large amount of Dinf methods determine steepest direction of fall
The information of acquisition.By planar curvature and steepest direction of fall, determining water (flow) direction just simultaneously consider the local gradient and
Hypsography information.
Summary of the invention
It is an object of the present invention in order to solve the flow direction that existing infinite flow direction method determines in bending landform, there are one
The problem of determining error, and the DEM for providing a kind of combination planar curvature and steepest direction of fall flows to estimation method, uses plane
Curvature is adjusted steepest direction of fall, and then determines water (flow) direction, is grid cell water flow in estimation digital elevation model
The method in direction.
The present invention is realized by following measure: a kind of DEM of combination planar curvature and steepest direction of fall flow direction is estimated
Meter method, wherein the following steps are included:
Step S1: load digital elevation model, it will be it needs to be determined that unit, use centered on the grid cell of water (flow) direction
The central point of center cell and 8 units adjacent thereto marks off 8 triangle projective planums, the most abrupt slope of more each plane
Degree chooses the maximum plane of steepest gradient value, records the plane, and using the corresponding gradient direction of the steepest gradient of the plane as
The steepest direction of fall of center cell;
Step S2: the planar curvature of 3 vertex units of triangle projective planum where calculating steepest direction of fall;
Step S3: the 4/ π angle with triangle projective planum limitation where steepest direction of fall is to allow variation range, uses step
The planar curvature for two downstream units that rapid S2 is calculated and the ratio of center cell planar curvature difference are to steepest descending side
To being adjusted.
Further, as a kind of digital elevation model of combination planar curvature and steepest direction of fall provided by the invention
Water (flow) direction estimation method advanced optimizes scheme, the equation of the step S2 Calculation Plane curvature are as follows:
Wherein z1,…,z9Distribution as shown in figure 4, wherein z1 ..., z9 indicate current computing unit and its 8, periphery phase
The elevation of adjacent unit, K are center unit z5Planar curvature.
Further, as a kind of digital elevation model of combination planar curvature and steepest direction of fall provided by the invention
Water (flow) direction estimation method advanced optimizes scheme, and the step S3 is to two downstream units being calculated in step S2
The ratio of planar curvature and center cell planar curvature difference is adjusted according to following equation progress steepest direction of fall:
As planar curvature K1And K2Value be one it is positive one it is negative when, modified water (flow) direction α*It is corresponding to be directed toward horizontal frontal plane curvature
Unit center, i.e., water flow abandon divergence unit be directed toward convergence unit, it may be assumed that if K1> 0 and K2≤ 0:
If K2> 0 and K1≤ 0:
I is the number that step S2 chooses triangle projective planum in formula, as planar curvature K1And K2Value with being positive or with being negative
When, use the planar curvature difference K of downstream units and center cell1-K0And K2-K0Ratio control rotation amplitude, determine rotation
Water (flow) direction α afterwards*Equation are as follows:
The direction is 0rad with surface, and increases clockwise;For α*Value may exceed allowed band the case where, need
It is modified, whenWhen,WhenWhen,It is finally flowed after amendment
To i.e. determination.
Further, as a kind of digital elevation model of combination planar curvature and steepest direction of fall provided by the invention
Water (flow) direction estimation method advanced optimizes scheme, the steepest gradient s of the triangle projective planum of the step S1 and corresponding slope
Degree direction α can be obtained by following equation:
In formula:
Wherein (x1, y1, z1), (x2, y2, z2), (x3, y3, z3) be triangle projective planum calculated three vertex three-dimensional
Coordinate will since from center point, steepest gradient direction may fall within outside triangular facet range, be modified to gradient direction
Gradient direction is adjusted to and has calculated the nearest triangular facet edge direction in direction, and synchronizes the gradient being revised as the direction gradient,
Modified direction αmAre as follows:
Wherein, in formula i be step S2 choose triangle projective planum number;For α*Value may exceed allowed band feelings
Condition need to be modified it, whenWhen,WhenWhen,After amendment really
Surely it eventually flows to.
The DEM flow direction is digital elevation model water (flow) direction.
The invention has the benefit that utilizing different descending positions present invention incorporates planar curvature and steepest direction of fall
The difference of horizontalization face curvature is adjusted steepest direction of fall, provides water (flow) direction in a kind of acquisition digital elevation model
Method;Compared to traditional method for being completely dependent on steepest direction of fall, this method has precision higher, to convergent main river
Road reduction effect is more preferable, considers the advantage of hypsography variation;The present invention is to carry out the quasi- water of water, soil, the defeated shifting formwork of solubility
Literary landform model provides the method for obtaining higher precision water (flow) direction, and also relying on digital elevation model can obtain than previous
The water (flow) direction estimated result of higher precision;The step of this method increases with respect to conventional method simultaneously is few, will not cause too many
Computer running time difference.
Detailed description of the invention
Fig. 1 is overall flow figure of the invention;
Fig. 2 is that 3 × 3 windows when steepest direction of fall calculates in the embodiment of the present invention divide schematic diagram, the center in figure
Point P0Two-dimensional coordinate is (0,0);
3 × 3 window elevation schematic diagrames when Fig. 3 is the midsagittal plane of embodiment of the present invention curvature estimation;
Fig. 4 is that steepest direction of fall needs the descending unit planar curvature K1 calculated and K2 pairs in the embodiment of the present invention after determining
The location drawing answered;
Fig. 5 is the digital elevation model in the embodiment of the present invention;
Fig. 6 is that eight triangular facets of calculative center cell and periphery adjacent cells composition are each in the embodiment of the present invention
From ruling grade schematic diagram;
Fig. 7 is Tunxi basin DEM topographic map used in the embodiment of the present invention;
Fig. 8 (a) is the main river figure obtained in the embodiment of the present invention using the method for Tarboton;
Fig. 8 (b) is the main river figure obtained in the embodiment of the present invention using the method for the present invention.
Specific embodiment
In order to clearly illustrate the technical characterstic of this programme, below by specific embodiment, this programme is illustrated.
Embodiment 1
Referring to Fig. 1 to Fig. 8, the present invention is: estimation method is flowed in conjunction with the DEM of planar curvature and steepest direction of fall,
In, comprising the following steps:
Step S1: load digital elevation model, it will be it needs to be determined that unit, use centered on the grid cell of water (flow) direction
The central point of center cell and 8 units adjacent thereto marks off 8 triangle projective planums, the most abrupt slope of more each plane
Degree chooses the maximum plane of steepest gradient value, records the plane, and using the corresponding gradient direction of the steepest gradient of the plane as
The steepest direction of fall of center cell;
Step S2: the planar curvature of 3 vertex units of triangle projective planum where calculating steepest direction of fall;
Step S3: the 4/ π angle with triangle projective planum limitation where steepest direction of fall is to allow variation range, uses step
The planar curvature for two downstream units that rapid S2 is calculated and the ratio of center cell planar curvature difference are to steepest descending side
To being adjusted.
Wherein, the equation of the step S2 Calculation Plane curvature are as follows:
Wherein z1,…,z9Distribution as shown in figure 4, wherein z1 ..., z9 indicate current computing unit and its 8, periphery phase
The elevation of adjacent unit, K are center unit z5Planar curvature.
Wherein, the step S3 is flat to the planar curvature and center cell of two downstream units being calculated in step S2
The ratio of face curvature difference is adjusted according to following equation progress steepest direction of fall:
As planar curvature K1And K2Value be one it is positive one it is negative when, modified water (flow) direction α*It is corresponding to be directed toward horizontal frontal plane curvature
Unit center, i.e., water flow abandon divergence unit be directed toward convergence unit, it may be assumed that if K1> 0 and K2≤ 0:
If K2> 0 and K1≤ 0:
I is the number that step S2 chooses triangle projective planum in formula, as planar curvature K1And K2Value with being positive or with being negative
When, use the planar curvature difference K of downstream units and center cell1-K0And K2-K0Ratio control rotation amplitude, determine rotation
Water (flow) direction α afterwards*Equation are as follows:
The direction is 0rad with surface, and increases clockwise;For α*Value may exceed allowed band the case where, need
It is modified, whenWhen,WhenWhen,It is eventually flowed to after amendment
Determine.
Wherein, the steepest gradient s of the triangle projective planum of the step S1 and corresponding gradient direction α can be by following equation
It obtains:
In formula:
Wherein (x1, y1, z1), (x2, y2, z2), (x3, y3, z3) be triangle projective planum calculated three vertex three-dimensional
Coordinate will since from center point, steepest gradient direction may fall within outside triangular facet range, be modified to gradient direction
Gradient direction is adjusted to and has calculated the nearest triangular facet edge direction in direction, and synchronizes the gradient being revised as the direction gradient,
Modified direction αmAre as follows:
Wherein, in formula i be step S2 choose triangle projective planum number;For α*Value may exceed allowed band feelings
Condition need to be modified it, whenWhen,WhenWhen,After amendment really
Surely it eventually flows to.
Embodiment 2
Referring to Fig. 1 to Fig. 8, the present invention also provides the DEM of combination planar curvature and steepest direction of fall to flow to estimation method,
Specifically includes the following steps:
Step S1: load digital elevation model, it will be it needs to be determined that unit, use centered on the grid cell of water (flow) direction
The central point of center cell and 8 units adjacent thereto marks off 8 triangle projective planums as shown in Figure 2, relatively each more flat
The steepest gradient in face chooses the maximum plane of steepest gradient value, records the plane, and by the corresponding slope of the steepest gradient of the plane
The steepest direction of fall of unit centered on degree direction;
The particular content of step S1 are as follows: by unit centered on the grid cell currently calculated, as shown in Fig. 2, in connection
The central point P of heart unit0With the central point (P of 8 adjacent cells around it1、P2、…、P8), it marks off such as wire frame solid in Fig. 2
8 triangle projective planums out, and if figure is that this 8 planes from 1 to 8 are numbered;
With P0The two-dimensional surface XY transverse and longitudinal coordinate of point is (0,0), and in addition the two-dimensional plane coordinate of 8 points is arranged such as Fig. 2 institute
Show;It assigns the height value that each grid cell has to its central point at this time, that is, knows P0To P8The elevation Z of this 9 points, then entirely
The XYZ three-dimensional coordinate of 9, portion point it is known that namely know each triangle projective planum three vertex three-dimensional coordinate;It can be used at this time
The steepest gradient s of each plane of following equation calculation and corresponding slope aspect α:
In formula:
Wherein (x1, y1, z1), (x2, y2, z2), (x3, y3, z3) be triangle projective planum calculated three vertex three-dimensional
The sequence of coordinate, 3 three-dimensional coordinates used herein will not influence as a result, there is no need to consider the sequence of three apex coordinates;
The gradient direction that equation (2) obtains is Circular measure, with surface to for 0rad, is increased clockwise;
Due to from central point P0It sets out, each triangular facet only has the allowed band of π/4, and steepest gradient direction may be fallen within
Outside allowed band, therefore gradient direction need to be modified, gradient direction is adjusted to and calculate the nearest triangular facet in direction
Edge direction, and synchronize and the gradient is revised as the direction gradient, modified direction αmAre as follows:
In formula: n is the number of corresponding triangle projective planum;Corresponding gradient s at this timemEquation is
In formula: h0For center unit elevation;haFor αmThe elevation of the object element of direction;R is center unit midpoint and αmMesh
The distance for marking unit midpoint, for being located at the object element of center cell positive direction, r value is equal to the grid side length of DEM, for position
In the object element of tilted direction, r value is equal toGrid side length.
Calculate separately the s of 8 triangle projective planumsmIt is worth and is compared, chooses wherein smIt is worth maximum triangle projective planum, with
The α of the planemThe steepest direction of fall α of unit centered on valuem *, and record triangle projective planum number;If there is multiple
Triangle projective planum has maximum smValue, then select to number the smallest triangle projective planum;
Step S2: the planar curvature of 3 vertex units of triangle projective planum where calculating steepest direction of fall is specific to calculate
Method are as follows:
3 × 3 window calculation planar curvatures formed with institute's computing unit and its surrounding cells are equally used, for such as Fig. 3
Shown in grid elevation distribution, central point Z5Planar curvature K are as follows:
In formula: wherein z1 ..., z9 indicate the elevation of 8 adjacent cells of current computing unit and its periphery, Z1-Z9It is Fig. 3
In in 3 × 3 windows 8 adjacent cells of center cell and its periphery elevation, Δ x is the side length of grid;
Step S3, it is to allow variation range with 4/ π angle of triangle projective planum limitation where steepest direction of fall, uses step
The planar curvature for 3 units that rapid S2 is calculated is adjusted steepest gradient direction, obtains final water (flow) direction, specifically
Are as follows:
The planar curvature of center cell is K0, in addition to center cell, 2 of selected triangle projective planum in step s 2
Vertex must have 1 one of 4 positive direction up and down for being in center cell, another is in upper left, lower-left, upper right, bottom right
One of 4 tilted directions;K is denoted as with the planar curvature of the vertex units of positive direction1, tilted direction unit planar curvature is K2;Such as Fig. 4,
If steepest direction of fall αm *In P1、P2、P0Composed triangle projective planum, K1It is then P1Planar curvature, K2For P2Plane
Curvature, K0For P0Planar curvature;Since planar curvature is demonstrated by the diverging and convergence of landform, planar curvature numerical value gets over megarelief
It more restrains, it is therefore desirable to rotate steepest direction of fall to the downstream direction of high planar curvature.
As planar curvature K1And K2Value be one it is positive one it is negative when, modified water (flow) direction α*It is corresponding to be directed toward horizontal frontal plane curvature
Unit center, i.e., water flow abandon divergence unit be directed toward convergence unit, be: if K1> 0 and K2≤ 0:
If K2> 0 and K1≤ 0:
I is the number that step S2 chooses triangle projective planum in formula.As planar curvature K1And K2Value with being positive or with being negative
When, use the planar curvature difference K of downstream units and center cell1-K0And K2-K0Ratio control rotation amplitude, it is specific to determine
Water (flow) direction α after rotation*Equation are as follows:
I is the number that step S2 chooses triangle projective planum in formula;For α*Value may exceed allowed band the case where, need
It is modified, whenWhen,WhenWhen,It is determined most after amendment
Flow direction eventually.
Illustrate technical characterstic of the invention to become apparent from, below by specific example, this programme is described in detail
Present invention determine that the process and advantage of water (flow) direction are as follows:
By taking digital elevation model shown in fig. 5 as an example, according to step 1, gray cell is connected with 8 units around it and is drawn
Divide triangle projective planum, the steepest gradient that each plane is calculated is as shown in Figure 6.It can be seen that in the ruling grade of 8 planes, number is
The numerical value of 4 triangle projective planum ruling grade is maximum, therefore steepest direction of fall is the direction of the plane, i.e. αm *=
2.840rad。
Two vertex Calculation Plane curvature for numbering the triangle projective planum for being 4 in addition to central point are chosen, center cell is located at
The planar curvature of forward direction, the unit of elevation 43.860m corresponds to K1, oblique positioned at center cell, the unit of elevation 43.103m is put down
Face curvature corresponds to K2, it is calculated according to equation (5), K0=-0.319, K1=-0.271, K2=-0.257.Using in step S3
Equation (6) obtain final water (flow) direction α*For 2.752rad.
Another specific example is as follows:
The DEM in Tunxi basin is chosen, as shown in fig. 7, using the steepest direction of fall method of Tarboton (1997) respectively
Determine that DEM unit flows to method of the invention, the confluence meter then proposed using Tarboton (1997) for such flow direction
Calculation method determines watershed concentration value, and extracts catchment area in basin shown in Fig. 8 and be greater than 4.5km2River.Use two kinds
Method determines that there are notable differences for boxed area in figure in the river obtained after water (flow) direction, use the side of (1997) Tarboton
The river that method obtains excessively ratio, and right side river does not conform to the trend turned back after being westwards substantially bent in field survey, and
The river for the flow direction reduction that the present invention obtains is closer to true river.
In conclusion having invented a kind of estimation digital elevation mould present invention incorporates planar curvature and steepest direction of fall
The method of type water (flow) direction, compared to traditional direct method using steepest direction of fall, this method has precision higher, right
Convergent main river reduction effect is more preferable, considers the advantage of hypsography variation, while this method increases with respect to conventional method
The step of it is few, the difference of too many computer running time will not be caused.
Technical characteristic of the present invention without description can realize that details are not described herein by or using the prior art, certainly,
The above description is not a limitation of the present invention, and the present invention is also not limited to the example above, the ordinary skill of the art
The variations, modifications, additions or substitutions that personnel are made within the essential scope of the present invention also should belong to protection model of the invention
It encloses.
Claims (4)
1. the DEM of a kind of combination planar curvature and steepest direction of fall flows to estimation method, which is characterized in that including following step
It is rapid:
Step S1: load digital elevation model, it will be it needs to be determined that unit centered on the grid cell of water (flow) direction, uses center
The central point of unit and 8 units adjacent thereto marks off 8 triangle projective planums, the steepest gradient of more each plane, choosing
The maximum plane of steepest gradient value is taken, records the plane, and will be centered on the corresponding gradient direction of the steepest gradient of the plane
The steepest direction of fall of unit;
Step S2: the planar curvature of 3 vertex units of triangle projective planum where calculating steepest direction of fall;
Step S3: the angle of π/4 with triangle projective planum limitation where steepest direction of fall is to allow variation range, uses step S2
The ratio of the planar curvature for two downstream units being calculated is adjusted steepest direction of fall.
2. the DEM of combination planar curvature according to claim 1 and steepest direction of fall flows to estimation method, feature exists
In the equation of the step S2 Calculation Plane curvature are as follows:
Wherein z1,…,z9Indicate that the elevation of 8 adjacent cells of current computing unit and its periphery, K are center unit z5Plane
Curvature.
3. the DEM of combination planar curvature according to claim 1 or 2 and steepest direction of fall flows to estimation method, special
Sign is, planar curvature and center cell planar curvature of the step S3 to two downstream units being calculated in step S2
The ratio of difference is adjusted according to following equation progress steepest direction of fall:
As planar curvature K1And K2Value be one it is positive one it is negative when, modified water (flow) direction α*It is directed toward the corresponding list of horizontal frontal plane curvature
First center, i.e. water flow abandon divergence unit and are directed toward convergence unit, it may be assumed that if K1> 0 and K2≤ 0:
If K2> 0 and K1≤ 0:
I is the number that step S2 chooses triangle projective planum in formula, as planar curvature K1And K2Value be positive or be negative when, make
With the planar curvature difference K of downstream units and center cell1-K0And K2-K0Ratio control rotation amplitude, determine rotation after water
Flow direction α*Equation are as follows:
The direction is 0rad with surface, and increases clockwise;For α*Value may exceed allowed band the case where, need to be to it
It is modified, whenWhen,WhenWhen,It is eventually flowed to i.e. after amendment
It determines.
4. the DEM of combination planar curvature according to claim 1-3 and steepest direction of fall flows to estimation method,
It is characterized in that, the steepest gradient s of the triangle projective planum of the step S1 and corresponding gradient direction α can be obtained by following equation
It arrives:
In formula:
Wherein (x1, y1, z1), (x2, y2, z2), (x3, y3, z3) sat for the three-dimensional of three vertex of triangle projective planum calculated
Mark, since from center point, steepest gradient direction may fall within outside triangular facet range, be modified to gradient direction, by slope
Degree direction is adjusted to and has calculated the nearest triangular facet edge direction in direction, and synchronizes the gradient being revised as the direction gradient, repairs
Direction α after changingmAre as follows:
Wherein, in formula i be step S2 choose triangle projective planum number;For α*Value may exceed allowed band the case where, need
It is modified, whenWhen,WhenWhen,It is determined after amendment final
Flow direction.
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CN111177917A (en) * | 2019-12-26 | 2020-05-19 | 西北农林科技大学 | Slope length extraction method based on SRTM |
CN112989639A (en) * | 2019-12-12 | 2021-06-18 | 河海大学 | DEM grid local drainage direction determination method based on averaging processing |
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CN107844757A (en) * | 2017-10-24 | 2018-03-27 | 河海大学 | A kind of method using river width in digital elevation model extraction basin |
CN108597022A (en) * | 2018-05-08 | 2018-09-28 | 河海大学 | A kind of method of small watershed inland river road width in estimation |
CN109492194A (en) * | 2018-12-29 | 2019-03-19 | 南京泛在地理信息产业研究院有限公司 | A kind of DEM second order terrain factor calculation method based on mathematic vector geometry |
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CN107844757A (en) * | 2017-10-24 | 2018-03-27 | 河海大学 | A kind of method using river width in digital elevation model extraction basin |
CN108597022A (en) * | 2018-05-08 | 2018-09-28 | 河海大学 | A kind of method of small watershed inland river road width in estimation |
CN109492194A (en) * | 2018-12-29 | 2019-03-19 | 南京泛在地理信息产业研究院有限公司 | A kind of DEM second order terrain factor calculation method based on mathematic vector geometry |
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CN112989639A (en) * | 2019-12-12 | 2021-06-18 | 河海大学 | DEM grid local drainage direction determination method based on averaging processing |
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CN111177917A (en) * | 2019-12-26 | 2020-05-19 | 西北农林科技大学 | Slope length extraction method based on SRTM |
CN111177917B (en) * | 2019-12-26 | 2021-11-02 | 西北农林科技大学 | Slope length extraction method based on SRTM |
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